Friday, 18 July 2014

Further thoughts on Phillips curves

In a post from a few days ago I looked at some
recent evidence on Phillips curves, treating the Great Recession as a test
case. I cast the discussion as a debate between rational and adaptive
expectations. Neither is likely to be 100% right of course, but I suggested the
evidence implied rational expectations were more right than adaptive. In this
post I want to relate this to some other people’s work and discussion. (See
also this post from Mark Thoma.)

The first issue is why look at just half a dozen years, in only
a few countries. As I noted in the original post, when looking at CPI inflation
there are many short term factors that may mislead. Another reason for
excluding European countries which I did not mention is the impact of austerity driven higher
VAT rates (and other similar taxes or administered prices), nicely documented by Klitgaard and Peck.
Surely all this ‘noise’ is an excellent reason to look over a much longer time
horizon?

One answer is given in this recent JEL paper by Mavroeidis, Plagborg-Møller and
Stock. As Plagborg-Moller notes in an email to Mark Thoma: “Our
meta-analysis finds that essentially any desired parameter estimates can be
generated by some reasonable-sounding specification. That is, estimation of the
NKPC is subject to enormous specification uncertainty. This is consistent with
the range of estimates reported in the literature….traditional aggregate time
series analysis is just not very informative about the nature of inflation
dynamics.” This had been my reading based on work I’d seen.

This is often going to be the case with time series
econometrics, particularly when key variables appear in the form of
expectations. Faced with this, what economists often look for is some decisive
and hopefully large event, where all the issues involving specification
uncertainty can be sidelined or become second order. The Great Recession, for
countries that did not suffer a second recession, might be just such an event.
In earlier, milder recessions it was also much less clear what the monetary
authority’s inflation target was (if it had one at all), and how credible it
was.

How does what I did relate to recent discussions by Paul
Krugman? Paul observes that recent observations look like a
Phillips curve without any expected inflation term at all. He mentions various
possible explanations for this, but of those the most obvious to me is that
expectations have become anchored because of inflation targeting. This was one
of the cases I considered in my earlier post: that agents always believed
inflation would return to target next year. So in that sense Paul and I are
talking about the same evidence.

Before discussing interpretation further, let me bring in a paper
by Ball and Mazumder. This appears to come to completely the opposite
conclusion to mine. They say “we show that the Great Recession provides fresh
evidence against the New Keynesian Phillips curve with rational expectations”.
I do not want to discuss the specific section of their paper where they draw
that conclusion, because it involves just the kind of specification
uncertainties that Mavroeidis et al discuss. Instead I will simply note that
the Ball and Mazumder study had data up to 2010. We now have data up to 2013.
In its most basic form, the contest between the two Phillips curves is whether
underlying inflation is now higher or lower than in 2009 (see maths below). It
is higher. So to rescue the adaptive expectations view, you have to argue that underlying inflation is actually lower
now than in 2009. Maybe it is possible to do that, but I have not seen that
done.

However it would be a big mistake to think that the Ball and
Mazumder paper finds support for the adaptive expectations Friedman/Phelps
Phillips curve. They too find clear evidence that expectations have become more
and more anchored. So in this sense the evidence is all pointing in the same
way.

So I suspect the main differences here come from interpretation. I’m happy
to interpret anchoring as agents acting rationally as inflation targets have
become established and credible, although I also agree that it is not the only
possible interpretation (see Thomas Palley and this paper in particular). My interpretation suggests that the New
Keynesian Phillips curve is a more sensible place to start from than the
adaptive expectations Friedman/Phelps version. As this is the view implicitly
taken by most mainstream academic macroeconomics, but using a methodology that does
not ensure congruence with the data, I think it is useful to point out when the
mainstream does have empirical support.

Some maths

Suppose the Phillips curve has the following form:

p(t) = E[p(t+1)] + a.y(t) + u(t)

where ‘p’ is inflation, E[..] is the expectations operator, ‘a’
is a positive parameter on the output gap ‘y’, and ‘u’ is an error term. We
have two references cases:

Static expectations: E[p(t+1)] = p(t-1)

Rational expectations: E[p(t+1)] = p(t+1) + e(t+1)

where ‘e’ is the error on expectations of future inflation and
is random. Some simple maths shows that under static expectations, negative
output gaps are associated with falling inflation, while under rational
expectations they are associated with rising inflation. If we agree that between
2009 and today we have had a series of negative output gaps, we just need to
ask whether underlying inflation is now higher or lower than in 2009.

3 comments:

In my opinion, a somewhat mixed approach is probably best. Adaptive expectations are a rule-of.thumb for people who don't pay attention to the economy, who don't care, who don't have the patience or capability to read economic data. Rational expectations require a certain background knowledge. Financial institutions like banks, insurance companies and big international companies certainly have the necessary information and through them, rational expectations are transmitted to consumers. This setup might explain the above average volatility of investment as well as the nominal wage downward rigidity during crises.

I refer only to INDEXED UNITS OF ACCOUNT: THEORY AND ASSESSMENTOF HISTORICAL EXPERIENCE by Robert J. Shiller February 1998 as one way out of what seems to be less of a problem (see Krugman blog July 23, 2013 'The Death of High Inflation').

I think that in your discussion of the evidence, the rational expectations hypothesis benefits very much from being the residual claimant. Basically, you note recent deviations from a simple model of autoregressive expectations. Given the choice between only two models, you may be right that, for the past 5 or 6 years the autoregressive model has fit US data very poorly.

However, there are many possible stories about expectations. I would like to look at elicited expectations and, in particular,the median response in the U Michigan Ipsos/ Reuters survey of US consumers.

https://research.stlouisfed.org/fred2/graph/?graph_id=185804

First I note that the simple autoregressive model fits the data extraordinarily well. I may be ignorant, but I think that the performance of the simple autoregressive model is incomprarably superior to that of any DSGE model. Second I note this is a pre-Friedman paleo Keynesian model.

Finally I admit that it fails at roughly sometime around January 20th 2009. However, the new pattern of expectations sure doesn't look like the REH. The survey median is not onlcy consistently higher than my guess based on lagged inflation (0.75% + 0.7*(lagged CPI inflation) but also consistently higher than the inflation the consumers were attempting to forecast. This looks to me like a gross rejection of the hypothesis that survey elicited forecasts are conditional means.

The forecasts also do not correspond to a credible official inflation target. They are consstently higher than the official inflation target. To me the graph does not suggest that the rational expectations assumption is working OK. It seems to me to show complete detachment from reality.

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